S t are positive integers (X +S) (x-t) is expanded - Simplified

The

answer

is x² + Kx-40 where K is a positive integer

work out the

out the smallest possible value of K

Given:

The expanded form of is .

Where, s, t, K are positive integers.

To find:

The smallest possible value of K.

Solution:

The expanded form of is . It means,

On comping both sides, we get

             ...(i)

K is a positive integer if s>t.

And

The factor pairs of 40 are (1,40), (2,20), (4,10), (5,8), (8,5), (10,4), (20,2) and (40,1).

Since s>t, therefore the possible values for (s,t) are (8,5), (10,4), (20,2) and (40,1).

Using (i), find the value of K for each factor pair.

Therefore, the smallest possible value of K is 3.